meaning - The usage of いや in response to questions

My question is about the usage and meaning of いや in response to questions. Take, for example, the 2 examples below.

1)

「僕たちは、もっと親睦を深める必要があると思うのでござるよ」

「いきなりどうしたのよ、何か思うところでも？」

「いや、常日頃から思っていたのでござるが、こう、色々と釈然としないのでござるよ」

2)

「ジューゾーくんも、盛り上げ役、ご苦労さま。　喉渇いたでしょう？」

木陰で休んでいたジューゾーに果汁を混ぜた冷水を渡し、ミントは目を細めて微笑う。

「いやぁ、折角こうして遠方から集まり、縁を得たのでござるから、仲良くなっておかねば損というもの！皆も楽しんでいるようで、一安心でござる」

From what I see, the usage of いや in response to a question like this can either mean "that's wrong/not true etc." i.e. saying that what the other person just said is not "correct", or it can be used as a sort of filler that comes at the start of a sentence similar to how one might use "well" in English. Looking at the above three lines I was thinking which one (or whether both) of these usages fits better. Since She asked him that and later in his response he gives a very vague and unspecific response by using 色々と(even though he clearly does as is evident very shortly afterwards). Or is it used as a sort of filler before he starts speaking, as he clearly didn't want to be asked this question (as is obvious from the way he answered it)?.

Can anyone clarify how いや is used in response to questions like this in general, and in this specific case?

Answer

In both cases, 「いや」 is used only as an interjection (a "filler" in your word), which is the equivalent of something like "well, um" or "well, you know". It does not really mean anything important.

We actually use this 「いや」 quite often in informal speech (mostly in speaking) just to create a momentary pause before making a statement. And from personal experience, I know Japanese-learners tend to take this 「いや」 to mean "no" by mistake.

Whether 「いや」 is being used as an interjection or as a casual "no" depends solely on the context. So, let us examine the context where 「いや」 is used in your examples.

1) Someone says to you 「いきなりどうしたのよ、何か思うところでも？」= "What's this about all of a sudden? Got something on your mind?"

Then you reply 「いや、常日頃から思っていたのでござるが、こう、色々と釈然としないのでござるよ。」= "いや、 I've always been thinking 'bout this, like, how things have kinda remained unexplained (between us)."

You indeed have something on your mind here, don't you? That is why this is not a place to say 'no'. That 「いや」 is a quintessential filler.

The quintessential fillers using 「いや」 often come in the forms:

「いや」、「いやね」、「いやな」、「いやいや」、「いやその」、「いやまあ」、「いや、それがね」、「いや、それがですね」、「いやあああ～」, etc.

Among those, 「いや」 and 「いやいや」 could be used as a casual 'no' depending on the context. Others will always be interjections.　(At least, I am being unable to think of an exception at the moment.)

2) You are only making a comment of your own will. Since you are not answering a question, that is no place to say 'yes' or 'no' in the first place. 「いやぁ」 is an interjection.

That is not a negative answer to the question 「喉渇いたでしょう？」 as 「いやぁ」 all by itself is nowhere near a natural negative answer to the question "Aren't you thirsty?"